Totally equimatchable graphs

نویسندگان

  • Jerzy Topp
  • Preben D. Vestergaard
چکیده

A subset X of vertices and edges of a graph G is totally matching if no two elements of X are adjacent or incident. In this paper we determine all graphs in which every maximal total matching is maximum.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stable Equimatchable Graphs

A graph G is equimatchable if every maximal matching of G has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph G edge-stable if G\e is equimatchable for any e ∈ E(G). After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartit...

متن کامل

Bounding the Size of Equimatchable Graphs of Fixed Genus

A graph G is said to be equimatchable if every matching in G extends to (i.e., is a subset of) a maximum matching in G. In a 2003 paper, Kawarabayashi, Plummer and Saito showed that there are only a finite number of 3-connected equimatchable planar graphs. In the present paper, this result is extended by showing that in a surface of any fixed genus (orientable or non-orientable), there are only...

متن کامل

Equimatchable Claw-Free Graphs

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable clawfree graph families. This characterization implies an efficient recognition algorithm.

متن کامل

Equimatchable Graphs are C_2k+1-free for k ≥ 4

A graph is equimatchable if all of its maximal matchings have the same size. Equimatchable graphs are extensively studied in the literature mainly from structural point of view. Here we provide, to the best of our knowledge, the first family of forbidden subgraphs of equimatchable graphs. Since equimatchable graphs are not hereditary, the task of finding forbidden subgraphs requires the use of ...

متن کامل

Equimatchable Graphs on Surfaces

A graph G is equimatchable if any matching of G is a subset of a maximum-size matching. From a general description of equimatchable graphs in terms of GallaiEdmonds decomposition [Lesk, Plummer, and Pulleyblank, "Equimatchable graphs", Graphs Theory and Combinatorics, Academic press, London, (1984) 239-254.] it follows that any 2-connected equimatchable graph is either bipartite or factor-criti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 164  شماره 

صفحات  -

تاریخ انتشار 1997